Results 261 to 270 of about 3,139,455 (314)

Structure Fault-Tolerant Hamiltonian Cycle and Path Embeddings in Bipartite $k$-Ary $n$-Cube Networks

IEEE Transactions on Reliability
One of the important issues in evaluating an interconnection network is to study the fault-tolerant Hamiltonian cycle and Hamiltonian path embedding problems. The $k$-ary $n$-cube (denoted by $Q^{k}_{n}$) networks are used as interconnection networks for
Eminjan Sabir, Jianxi Fan, J. Meng, B. Cheng   +3 more
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Finding Hamiltonian Cycle in Graphs of Bounded Treewidth

The Sea, 2018
The notion of treewidth, introduced by Robertson and Seymour in their seminal Graph Minors series, turned out to have tremendous impact on graph algorithmics.
Michal Ziobro, Marcin Pilipczuk
semanticscholar   +1 more source

Hamiltonian Cycles and Markov Chains

Mathematics of Operations Research, 1994
In this paper we derive new characterizations of the Hamiltonian cycles of a directed graph, and a new LP-relaxation of the Traveling Salesman Problem. Our results are obtained via an embedding of these combinatorial optimization problems in suitably perturbed controlled Markov chains.
Filar, JA, Krass, D
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Detecting Hamiltonian cycles

Applied Mathematics and Computation, 1992
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Hamiltonian Cycles of Adjacent Triples

Studies in Applied Mathematics, 1980
A construction is given for ordering triples chosen from an ordered set of elements, so that each triple agrees with each neighbor in two of its members and has third member that is a neighbor of its neighbor's third member. Neighbors here are adjacent in order, and also the first is neighbor to the last among both elements and triples.
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A Remark on Hamiltonian Cycles

Mathematische Nachrichten, 1992
AbstractLet G be an undirected and simple graph on n vertices. Let ω, α and χ denote the number of components, the independence number and the connectivity number of G. G is called a 1‐tough graph if ω(G – S) ⩽ |S| for any subset S of V(G) such that ω(G − S) > 1.
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Hamiltonian Cycles and Tight Cutsets

Graphs and Combinatorics
Let \(G\) be a graph. A cutset \(S\) of \(G\) is tight if \(|S|=c(G-S)\). The authors define a reduction step in \(G\) to be the deletion of all edges joining two vertices that lie together in a tight cutset, making each tight cutset independent. The (Hamiltonian) reduction \(R(G)\) of a 1-tough graph \(G\) is the iterative application of reduction ...
Viswanathan B. N, Douglas B. West
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Non‐Hamiltonian Cycles in Tournaments

Journal of Graph Theory
ABSTRACTA cycle is said to be directed if all its arcs have the same direction. Otherwise, it is said to be nondirected. A strong tournament is a tournament containing a directed path from any vertex to any other vertex. A tournament that is not strong is said to be reducible.
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Essential independent sets and Hamiltonian cycles

Journal of Graph Theory, 1996
A set \(S\) of vertices in a (finite, undirected, simple) graph \(G\) is said to be essential independent iff \(S\) is independent and contains two distinct vertices the distance of which is two in \(G\). Denoting the degree of a vertex \(x\) in \(G\) by \(d(x)\) the author proves the following theorem: Let \(k\geq 2\) and \(G\) be a \(k\)-connected ...
Chen, Guantao, Egawa, Yoshimi, Liu, Xin, Saito, Akira   +3 more
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The Square of a Hamiltonian Cycle

SIAM Journal on Discrete Mathematics, 1994
All graphs considered in this paper are simple and undirected. For a given graph \(G= (V,E)\) we denote by \(\delta(G)\) the minimum degree of \(G\). A \(k\)-chord of a cycle \(C\) is an edge joining two vertices of distance \(k\) on \(C\). The \(k\)th power of \(C\) is the graph obtained by joining every pair of vertices with distance at most \(k\) on
Fan, Genghua, Häggkvist, Roland
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